Speaker
Description
In this talk we extend the work of Deckelnick et al. (arXiv.2301.08690) to shape optimization with parabolic PDE constraints, where we consider time-dependent as well as time-independent domains. We use the method of mappings and consider steepest descent and Newton-type directions for the solution of the underlying optimization problems. The appearing PDEs for the state and the adjoint are formulated using a least-squares space-time approach requiring only minimal regularity. The descent directions for the shape transformations are computed in the Lipschitz topology, where the respective linear programmes are numerically solved with an interior point method. We illustrate our approach at hand of a selection of numerical examples which demonstrate the performance of the method.
